论文标题
Dicke州准备工作的短深度电路
Short-Depth Circuits for Dicke State Preparation
论文作者
论文摘要
我们提出了短时的电路，以确定性地准备任何DICKE | dn，k>，这是所有N Qubit量计算基础状态的同等振幅叠加，并具有锤击权重k。迪克国家是一类重要的纠缠量子状态，具有多种应用，并且是物理系统中实验创造的悠久历史。另一方面，对于在逼真的量子计算硬件连接性上进行DICKE状态准备的有效可伸缩量子电路的知之甚少。 在这里，我们为DICKE状态提供了准备电路| Dn，K>带（i）o（k log（n/k））的深度（例如，在当前的离子陷阱设备上）； （ii）o（k sqrt（n/k））的深度= o（sqrt（nk），用于欧米茄（SQRT（n/s））X O（sqrt（n/s））X O（sqrt（ns））的网格连接性，带有s <= k（例如，电流超导量Qubit Decesties）。 两种方法的总门计数为O（kN），不需要Ancilla Qubits，并且概括了对称纯状态的制备和压缩，其中所有非零幅度在，其中所有非零幅度对应于最多k的均值k。因此，我们的工作显着改善并扩展了先前的最新电路，这些电路在任意K的线性最接近的邻居连接（计算理论的基础2019）和深度O（log n）上具有k = 1的全能连接性（Advanced Quantum Technologies 2019）。
We present short-depth circuits to deterministically prepare any Dicke state |Dn,k>, which is the equal-amplitude superposition of all n-qubit computational basis states with Hamming Weight k. Dicke states are an important class of entangled quantum states with a large variety of applications, and a long history of experimental creation in physical systems. On the other hand, not much is known regarding efficient scalable quantum circuits for Dicke state preparation on realistic quantum computing hardware connectivities. Here we present preparation circuits for Dicke states |Dn,k> with (i) a depth of O(k log(n/k)) for All-to-All connectivity (such as on current ion trap devices); (ii) a depth of O(k sqrt(n/k)) = O(sqrt(nk) for Grid connectivity on grids of size Omega(sqrt(n/s)) x O(sqrt(ns)) with s<=k (such as on current superconducting qubit devices). Both approaches have a total gate count of O(kn), need no ancilla qubits, and generalize to both the preparation and compression of symmetric pure states in which all non-zero amplitudes correspond to states with Hamming weight at most k. Thus our work significantly improves and expands previous state-of-the art circuits which had depth O(n) on a Linear Nearest Neighbor connectivity for arbitrary k (Fundamentals of Computation Theory 2019) and depth O(log n) on All-to-All connectivity for k=1 (Advanced Quantum Technologies 2019).
